Digital filters are commonly employed in signal processing applications. U.S. Pat. No. 5,983,254 to Azadet discloses a number of known finite impulse response (FIR) filter implementations. For example, FIG. 1 shows an FIR filter in the hybrid form. The hybrid form has a reduced number of delay elements overall (relative to the direct and transpose forms), with delay elements in both the input and output paths. The exemplary conventional hybrid FIR filter 100 shown in FIG. 1 has three modules 110-1 through 110-3. Each module, such as module 110-1, provides three taps at multipliers 115-1, 115-2 and 115-3, respectively. Each module 110 includes the same number of delay elements as the number of taps. The delay elements may be embodied, for example, as shift registers. Specifically, delay elements 105-1 and 105-2 are disposed on input path 101, and delay element 105-3 is disposed on output path 111. Delay element 105-2 is inserted between multipliers 115-1 and 115-2. Delay element 105-2 is inserted between multipliers 115-2 and 115-3. Adder 120-3 receives a delayed sum generated by adder 120-4 and a product generated by multiplier 115-3 and generates a sum. Adder 120-2 receives the sum generated by adder 120-3 and a product generated by multiplier 115-2 and generates a sum. Adder 120-1, disposed on output path 111, receives the sum generated by adder 120-2 and a product generated by multiplier 115-1 and generates a sum.
The filter weights for the modules 110-1 through 110-3 shown in FIG. 1 are scalar values, w0 through w8. With the above filter arrangement, the z-transform of the transfer function of filter 100, H(z), can be expressed as follows:H(z)=z−1{w0+w1z−1+w2z−2}+z−3{w3+w4z−1+w5z−2}+  (1)where the first term z−1{w0+w1z−1+w2z−2} corresponds to module 110-1; and the second term z−3{w3+w4z−1+w5z−2} corresponds to module 110-2. It can be shown that the hybrid form FIR filter 100 shown in FIG. 1 is functionally equivalent to a direct form FIR filter and a transpose form FIR filter (although, beneficially, with fewer delay elements). For a more detailed discussion of such FIR filters, see, for example, U.S. Pat. No. 5,983,254, incorporated by reference herein.
A number of applications require multi-dimensional signals to be processed on FIR filters, such as the FIR filter 100 shown in FIG. 1. For example, two-dimensional and three-dimensional signals are often processed using FIR filters in image filtering and video processing applications. Each dimension of the multi-dimensional signal, however, is typically processed independently. Frequently, however, redundancies result from the same operation, such as a delay, being applied to the same input signal multiple times as each dimension is independently processed. For example, conventional cross-talk cancellers typically consider the same signal on a given twisted pair multiple times in order to reduce the echo on the same twisted pail, as well as the near end cross-talk on each of the other twisted pairs. In the case of four twisted pairs, for example, there is a factor-of-four redundancy, since a given signal is used once for the echo cancellation on the same twisted pair and three additional times for the near end cross-talk on the other three twisted pair. Such redundancies unnecessarily consume circuit area and power. A need therefore exists for multi-dimensional FIR filters that reduce the number of redundancies.